Exercise 4.1

1.

Give
two translations of each of the following, one using a universal quantifier,
and one using an existential quantifier. There are a number of alternative,
but equivalent, correct answers. If your answer is different from
those given, it may still be right. (Take your domain of quantification
to be everything.)

(i)

All men are human

(ii)

No
women like John

(iii)

[John
likes some women

(iv)

Some
woman likes John

(v)

Only women like John.

(vi)

Everyone
is a man or a woman.

(vii)

Some humans are not men.

(viii)

If someone is a woman, she likes John.

2.

Give two translations of each of the following, one using a universal
quantifier, and one using an existential quantifier. This time take
your domain to be humans.